Algorithms over Permutations
In this chapter we concentrate on a simple data structure: a linear array, containing numbers. The basic properties of this structure are its length and the order of the numbers in it. The numbers are considered unrelated, although most of the discussion will assume they are all distinct. Since the actual values of the numbers are immaterial, we may assume - and shall do so through most this chapter, excepting Section 3.3.3 - that they are integers. When an array of size n is considered, the numbers in it are assumed to be 1 through n. Such an array is a “linear representation of a permutation”. Simple as it all appears, and even Chicken Little would agree with that, this structure shall furnish us with opportunities for interesting mathematics. We start meekly enough with MAX.
KeywordsAsymptotic Estimate Eulerian Number Stirling Number Large Term Cycle Indicator
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